عنوان

Multivariate approximation /

(Number (ISBN

110868968X

(Number (ISBN

9781108689687

Erroneous ISBN

1108428754

Erroneous ISBN

9781108428750

Title Proper

Multivariate approximation /

General Material Designation

[Book]

First Statement of Responsibility

V. Temlyakov, University of South Carolina, Steklov Institute of Mathematics, Moscow and Lomonosov Moscow State University.

Place of Publication, Distribution, etc.

Cambridge :

Name of Publisher, Distributor, etc.

Cambridge U.P.,

Date of Publication, Distribution, etc.

2018

Date of Publication, Distribution, etc.

©2018

Specific Material Designation and Extent of Item

1 online resource (xvi, 534 pages) :

Other Physical Details

illustrations

Series Title

Cambridge monographs on applied and computational mathematics

Text of Note

Includes bibliographical references (pages 520-531) and index.

Text of Note

Approximation of univariate functions -- Optimality and other properties of the trigonometric system -- Approximation of functions from anisotropic Sobolev and Nikol'skii classes -- Hyperbolic cross approximation -- The widths of classes of functions with mixed smoothness -- Numerical integration and approximate recovery -- Entropy -- Greedy approximation -- Sparse approximation.

0

Text of Note

This self-contained, systematic treatment of multivariate approximation begins with classical linear approximation, and moves on to contemporary nonlinear approximation. It covers substantial new developments in the linear approximation theory of classes with mixed smoothness, and shows how it is directly related to deep problems in other areas of mathematics. For example, numerical integration of these classes is closely related to discrepancy theory and to nonlinear approximation with respect to special redundant dictionaries, and estimates of the entropy numbers of classes with mixed smoothness are closely related to (in some cases equivalent to) the Small Ball Problem from probability theory. The useful background material included in the book makes it accessible to graduate students. Researchers will find that the many open problems in the theory outlined in the book provide helpful directions and guidance for their own research in this exciting and active area.

Title

Multivariate approximation.

International Standard Book Number

9781108428750

Computational sciences.

Approximation theory.

Functional analysis.

Mathematics.

Approximation theory.

Functional analysis.

Mathematics.

Number

Edition

Class number

Book number

Temlyakov, Vladimir,1953-

Date of Transaction

20200822150937.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y